Answer:
95 %
99.7 %
Explanation:
= 166 cm = Mean
= 5 cm = Standard deviation
a) 156 cm and 176 cm


From the empirical rule 95% of all values are within 2 standard deviation of the mean, so about 95% of men are between 156 cm and 176 cm.
b) 151 cm and 181 cm


The empirical rule tells us that about 99.7% of all values are within 3 standard deviations of the mean, so about 99.7% of men are between 151 cm and 181 cm.
We will find the mass from
mass = density x volume
We are told the density and must find the volume from the dimensions given
the volume of the washer will be the area x thickness (remembering to convert all measurements to meters)
if the washer had no hole, its area would be pi (0.0225m)^2 (remember to convert to meters and to use radius)
the area of the hole is pi(0.00625m)^2
so the area of the washer is pi[(0.0225m)^2 - (0.00625m)^2] = 1.5x10^-3 m
the volume of the washer is 1.5x10^-3 m x 1.5x10^-3 m = 2.25x10^-6 m^3 (the thickness of the washer is 1.5 mm = 1.5x10^-3m)
thus, the mass of the washer = 8598kg/m^3 x 2.25x10^-6m^3 = 0.0189kg = 18.9 grams
Answer: C. Some of uranium's mass is converted into energy, so the smaller atoms have less mass.
Explanation:
From Einstein's mass-energy relation:
E = mc²
Mass and energy are equivalent. Mass can be converted into energy and energy into mass.
When Uranium atoms under go nuclear fission, smaller atoms are formed and huge amount of energy is released. This energy comes from the mass difference of the uranium nuclei and new nuclei formed. This mass converted into energy according to Einstein's equation.
The minimum speed with which Captain Brady had to run off the edge of the cliff to make it safely to the far side of the river is around 6 meters per second.
<h3>Further explanation</h3>
This is a free fall 2-dimensional type of problem, therefor we can write equations for both dimensions which model the fall of captain Brady. Let's call <em>x </em>the distance travelled by the captain on the horizontal direction and <em>y </em>the distance travelled on the vertical direction.
Lets suppose that Brady jumped with a complete horizontal velocity from a point which we will call the origin (meaning zero horizontal and vertical displacement), and let's call <em>ta</em> the time it took for captain Brady to reach the river (meaning the time he spent on the air). The equations of motion for the captain will be:


We know that at time <em>ta</em> the captain would have traveled 6.7 m on the horizontal direction, and 6.1 m in the vertical direction. Therefor we can write that:


Which gives us a system of 2 equations and 2 unknowns (<em>V</em> and <em>ta</em>). From the second equation we can solve for <em>ta</em> as:

And solving for <em>V</em> on the first equation, we find that:

Which is almost 6 meters per second.
<h3>Learn more</h3>
<h3>Keywords</h3>
Free fall, projectile, gravity
Answer: d. I or II
Explanation: A traveling wave has speed that depends on characteristics of a medium. Characteristics like linear density (μ), which is defined as mass per length.
Tension or Force (
) is also related to the speed of a moving wave.
The relationship between tension and linear density and speed is ginve by the formula:

So, for the traveling waves generated on a string fixed at both ends described above, ways to increase wave speed would be:
1) Increase Tension and maintaining mass and length constant;
2) Longer string will decrease linear density, which will increase wave speed, due to their inversely proportional relationship;
Then, ways to increase the wave speed is
I. Using the same string but increasing tension
II. Using a longer string with the same μ and T.